Lost in translation

1. Lost in translation Demystifying mathematical writing 9th IWACC Austin, TX Patrick Bahls, UNC Asheville Department of Mathematics

2. Why is writing �in math� so hard? Unfamiliar notation Daunting terminology Unfamiliar genres definition proposition proof

3. Overcoming notation Much mathematical notation can be read as �shorthand� for equivalent expressions in one�s native tongue. Examples. �=� is read, literally, �equals�; similarly, �?� is read �does not equal.�

4. Mastering terminology While mathematical terminology can seem overwhelming (especially to the intermediate math major)� �even the densest of math terminology has the advantage of precision and unambiguousness.

5. Writing like a mathematician As in any other academic field, in mathematics aspiring writers encounter genres specific to the discipline, and these genres play many of the same roles (exposition, persuasion, etc.) Moreover, mastery of these genres can be achieved through the same means as in other fields: practice, feedback, and iteration.

6. New styles and structures Definitions are straightforward declarations of meaning, much as one would find in a dictionary. Propositions are statements of fact, involving both hypothesis and conclusion.

7. Proof Proof comprises a sequence of logical inferences that proceed from hypothesis to conclusion in some mathematically acceptable fashion.

8. But is it good? Assessing the quality of mathematical writing takes practice, but it helps to know that the same elements distinguishing good writing in other academic fields serve the same role in mathematics.

9. An exercise Take a moment to brainstorm characteristics of good academic writing in a field with which you�re familiar.

10. What makes for a good proof? Correctness Completeness Clarity Composition

11. Students� sense of right and wrong Intermediate-level math students are quite good at being able to identify these qualities in non-mathematical writing. Structured exercises can help them make the same distinctions regarding proofs.

12. Another exercise Examine the given �student� responses to a political science professor�s prompt: You are a senior adviser to Ralph Nader as he undertakes another bid for the presidency. Prepare a two-minute statement to be delivered on a nationwide radio talk show defending Mr. Nader against those who accuse of him of being a �spoiler.�

13. A cognate exercise Now examine the �student� responses to the following mathematical problem: Prove that the sum of two even numbers is even.

14. In the classroom� As early as the second week of class, students in an �introduction to proofs� course are able to discern (initially somewhat intuitively) which of a set of mathematical proofs is strongest, which is weakest.

15. Refining intuition Throughout the semester, students can be challenged to develop their ability to assess the quality of their own and others� mathematical writing, and to gain the authority to perform their assessment.

16. One last example At mid-semester in my �introduction to proofs� course, my students are asked to assess the quality of professional mathematicians� proofs drawn from textbooks with which they are often familiar.

17. Student response Data from our current study on writing assessment indicates that students found these exercises very helpful. Students also indicated that the attention paid to mathematical writing helped them to improve their writing in other courses.

18. Student gains I know how to evaluate and revise my writing according to standards in the field of mathematics: 44.3% gain in mean I am confident in my knowledge of the rules for writing in mathematics: 42.2% gain in mean I am aware of different ways of organizing a paper appropriate to mathematics: 46.1% gain in mean

19. Of the same cloth Many differences between writing in math and writing in other fields are illusory Writing in math plays some of the same roles as (and takes similar form to) writing in other disciplines Good math writing exhibits many of the same characteristics as does good writing elsewhere